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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 1
# Folio 22v, page id 00068203:0044
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fig. 16. pascul. 44) eiaimeter. () RadiutB. Bai Quidratum diametri (2 a) quad. insciptum (R4 2 a) Radis tlticis
idem producitur
summa sinuum
ejus dimudium 47, R42, a = Rq Z, a. 7B = a = B4  a. Ducatur ZB in arcum gB.
peripheria verantem.
Erit portro superficiei colndrice, cujus basis circulus AB.  altitudo ipsa ZB.
ponatur ZB. duci in totam peripteriam, manisestum est cylindrum, cujus est ea superficies fieri
ex ductu circuli in buseos in altitudinem cylindri. Radius est a. Esto Peripheria X. erit cirtu
circulgs: aX. et Z Cylinder erit a_, a = gL, a, = ax - a X 19L, - ax -a  = ap a
Area cylindri divisa per bacu semibacim, radium basCos AB- a. producto duplicato dabit superficim
r cylindri, totam cujs octava pars est, dicta portu  quaesita ergo dividatur per radium, producti,
colum est ax  ause
B equo
a 94 
eir al
sumatur pars, quarta ax = aX ab hac si aufeatur summa Sinuum versorum
R9128
dupt: Jam quia segmentum circuli majoris non potest commode auferri a minori auferatur a majore
28 1b B432
rertabit.
ax ax
vel AZ
XG. XD ed sou cegmentum, duplicatum,  duplicatum, restabit summa sinuum rectorum DR. DZ. BB
Segmentum daplientum est
ax ax =
ratur ab
na
et a Residuo auferatur differentia inter majorem et minorem. Nam si cauferre debeam _b ab a
idem est ac sianferam ib a C. quod esse suppono majus quam a. et a resituo auferam diffe
rentram inter C et a. a - b = 4 - b, - ( +a Pomo segmento duplicato PB. ablato a
circulo AB. rectabit seminirulus aX + duo Triangula octantis circuli tubra. Ab hoc
residuo auferenda est differentia inter aX et a+ - ad
rectabit
s
F R4128
aX + aX hoc auferatur a ax + 2 Y la octorrtis AB. tam av- 2ap.
R9128
Restabit: 2 Da octantis AB = ax
ax. Ut autem investigemus Flum octantis hubemus
n4 128
rectum 2Z = vel ZY. = Rq a. Xeius quadrato  a. aufert Ltum de ZB. a + 1a = 2a 9.
habemus 2a - 2a RqL, hujus Rq. est Recta (QB) Y2a- 2a nai erit
2a= 2a  2 23 auferatur a quod. radi a. restalit etum fuleri Ergo fulem erit quod
a a erit a-
2a - 2 a Mq=
2a+ 2a 21
Et fulcrum eii
a + 2a _42 suppue fulem aequari recter 4 B) ducatur sim oimidiua satr sea in dimido
 productu
erit quadruli ZB. dimedium ducatur in QB. productum erit Rg 4a Aa
a-4a
=
ea
a - a
=p
R432
42.
Jam omnes sinus DI. aequantur radio a. ducto in DA vel 2Q - a9: a fiet (R91 a.) summa simumu
64
32 1
a qu auferatur recta ZA vl (vel 22) dacta in arcum, ZB vel 8 fiet q ax, restabit.
R4L a = = na: C ax = - 2a a X - ax. Ergo (quia B1 =  a x- aX ) erit a = 2a - a +
X432, ∞ R4128
ecesseest errorem esse in calulo, quia a H 2a
1g 32
A912B
AG2 932 8
Fortasse datur Meterodus in arithmetica infinitorum, summandi aliquam surdorum progressionem, quoniam
etsi praecise integris expituri non possint, for aliquando tamen id quod dast deest, erit minus quolibet
dato. vig. quoties res reduri st ad eum statum, ut radios quadratae differentiamm aut aliquid
ab illis pendens desit supersitque ed enim tuto negligi potest
R4 a. + R9 b. Rg a + b. + 2ab.
Ag ab. + Rq bC = RqC ab + b  + 2Rq abC
aq a e a rbC + Ru d + bC = Rg. a +bC + d + bc + Rq bc +bca +d bc +de
quotres mmilliplicave duarm surdarum in se invice aliquis terminus produci potest,
ex quo possit extrahi radix, suve quadrata sive cubicae. toitres ex diubus
sundis fieri st una.
differentius inz dias radices quadratas semper exprim potest me radiae quaditta ugq Ab
est, ineatur summa quadratorum, eaque duplicetur producto addatu
erit summo Radicno. Jamsi his radices summare velis,
R9 ad + A4 V, Rq prinae duae R9 a +b- (4a R9b + RqC-
Ra 14qa + ab = 2B aqu 14b.  4 14 2ac + b
a - Rq a
ax - Ba
nana
a - R4
1 = X
isa 
in aer se tuo toee
2 a
a anfenti
F9B R4128
Aota sii velis inire summam quadratorum, sic procedendum ab= bc:
summa quadratum differentiarum inter radices, residuo quadia tradis
eaa
Rg2 AquE Bq2
24 12
B432
ac p
ad + +0 = =Lttqu - 1qu
Nam Aa ab RquC
Rg ab. - (ebc
4gabbc + bca
Xa = 2 = A
aa - = A + y
B = A + Y
B- A = . eeam